Just designing a new lab using Vernier's "Go Motion" rotational motion
sensor. It gives readings for angular position and angular velocity at
regular intervals. I'm having a little trouble understanding a statistical
method that one of our instructors would like to use.
The experiment starts with a single spinning disk. The student then drops
a second disk on the first (effectively doubling the moment of inertia).
We're collecting 20 data points per second. The interaction takes about a
quarter of a second. Students take the 5 data points before and the 5
points after the "collision" and look at the mean angular velocity for
each. It's also easy to calculate a variance for the 5 points.
Here's the rub. The variance on the mean should properly be calculated as
sigma/sqrt(n) for a selected set of random samples. But I don't think that
is valid in this case because the samples are correlated. Vernier's
software may even be doing some smoothing and approximation for angular
positions that fall between the position encoder's discrete digitization
steps.
We're getting results that seem to show remarkable precision but our Z
values for the conservation of angular momentum are huge. Can I justify
simply using the variance on the five data points? Should I look for
another measure of the precision of our angular velocity measurements?
Paul
(Yes, I know this will send John into tirade. I'm looking forward to it.)